Additive mappings that preserve rank one nilpotent operators

✍ Scribed by Wu Jing; Pengtong Li; Shijie Lu

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 113 KB
• Volume: 367
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(02)00617-1

✦ Synopsis

Let B(X) be the algebra of bounded operators on a complex infinite dimensional Banach space X, and F (X) be the subalgebra of all finite rank operators in B(X). A characterization of additive mappings on F (X) which preserve rank one nilpotent operators in both directions is given. As applications of this result, some additive preservers are described.